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This question already has an answer here:

You're working in a bank and you've been given ten piles of coins. One of the piles, you've been told is a pile of fake coins. The real coins are 100g in weight, while the fake coins are just 90g.

Now, you want to spend the least amount of time weighing the coins to get on with the rest is of your job, so what is the least amount of weighings to identify the fake pile of coins?

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marked as duplicate by f'', Tryth, Rand al'Thor, mmking, Spikatrix Jul 4 '15 at 12:35

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We can find the pile of fakes

in just one weighing.

From the first pile, take one coin, from the second pile take 2 coins, from the third pile, take 3 coins and so on. The total number of coins would be 55, and the expected weight would be 5500 grams. The weight will be short by 10 grams per fake coin. So dividing the weight difference by 10 will give us the number of fake coins in our sample set, which will be the same as the pile number we assigned. (If it's 10 grams short, the first pile is fake, if it's 20 grams short, the second pile is fake, if it's 30 grams short, the third pile is fake and so on.)

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  • $\begingroup$ best answer !!! $\endgroup$ – ilaiya Jul 4 '15 at 12:01

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